I had used Types to create a custom type, and custom menu item for the different taxonomies, and thee dropdown located in the main nav menu worked just fine.

A couple weeks ago, the site was updated to WordPress 3.5, and that dropdown stopped working on all iOS devices, but it still works on desktop browsers, and I cannot figure out what caused the break. We have not yet updated the site to 3.5.1, but it is running the newest version of Types.